Electromagnetic transient (EMT) simulation is essential for transient stability analysis in renewable energy power systems, but its high computational cost limits large-scale scenario screening, control tuning, and rapid post-event assessment. This paper presents a surrogate-assisted EMT-based approach to enhance the efficiency of transient stability studies, where data-driven surrogate models are used to assist, rather than replace, EMT simulations. Three representative EMT-based tasks are investigated. For pre-event analysis, voltage-observable surrogate models are used to approximate EMT-derived severity indicators and support efficient vulnerability ranking. For in-event analysis, surrogate-assisted ordinal optimization is employed to tune converter control parameters to improve fault ride-through performance. For post-event analysis, stability-diagnosis models are developed using externally measurable voltage waveforms to detect instability and identify parameter interactions that influence it. Case studies on a representative renewable energy power system show that the proposed approach substantially reduces the number of EMT simulations while preserving key nonlinear transient characteristics relevant to stability assessment.